The Diffusion Problem of Toxic Gases in a Tunnel. The Pump Absorption Model

In this work we study the diffusion of a toxic gas in a tunnel due to an explosion in order to realize a control system-via a wireless network of active sensors-for identification and immediate containment procedures. To this end an aspiration pump is turned on instantaneously at a distance of b meters from the explosion to mitigate the effects of the terroristic act. We exactly find the diffusion concentration in order to provide a solution useful for comparison to other models: numerical ones or models with many aspiration pumps. The model is described by the diffusion partial differential equation (PDE) with a non-homogeneous term which models the aspiration pump. A model with more suction pumps is outlined.